Question

Mrs. Stevens wants to have $18,000 in the bank in 3 years. If she deposits $9500 today at 4% compounded quarterly for 3 years, how much additional money will she need to add after three years to her investment to make her balance $18000?
a.
$8356.79
b.
$0
c.
$7295.16
d.
$10,704.84

Answer 1

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \qquad \begin{cases} A=\textit{current amount}\\ P=\textit{original amount deposited}\to &\ 9500\\ r=rate\to 4\%\to \frac{4}{100}\to &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, 4 quarters a year} \end{array}\to &4\\ t=years\to &3 \end{cases}$

so.. if she deposits a principal of 9,500 today, compounding quarterly for 3 years, she'll have A amount

how much additional amount?  well, 18,000 - A

Answer 2

A=p(1+i/m)^mn
A=9,500×(1+0.04÷4)^(4×3)
A=10,704.84
The balance she needs

18,000−10,704.84
=7,295.16